The Messenger of Allah ﷺ took a bath and offered two rak'ahs of prayer and said the dawn prayer. I do not think he performed ablution afresh after taking a bath. (Using translation from Abū Dāʾūd 250)
كَانَ رَسُولُ اللَّهِ ﷺ «يُصَلِّي الرَّكْعَتَيْنِ قَبْلَ صَلَاةِ الْغَدَاةِ وَلَا أَرَاهُ يُحْدِثُ وُضُوءًا بَعْدَ الْغُسْلِ»